A typical parametric engineering model might contain thousands of variables and constraints (or “equality relations”). When combined with the sets of feasible variable values, the resulting combinatorial explosion can result in an enormous trade space, in some cases involving thousands to billions of alternative configurations. Exhaustive search of such trade spaces is often infeasible. Even when possible, manually sifting through so many cases is often impractical. Furthermore, even automated systems require guidance to determine where to focus the search for good designs. In the absence of a domain expert or experienced user, the need exists for some means to narrow the trade space in accordance with user input constraints so as to focus the analysis on the areas of interest.
Constraint management systems (CMS) can provide such focus when combined with automatic robust non-linear algebraic equation solvers. Such hybrid systems merge the concepts of “input parameters” and “output parameters” into a single parameter set from which the user is free to choose which parameters will be treated as inputs for any given trade study, leaving the rest to be computed by the constraint network. This choice can be made at runtime (subject to mathematical feasibility), allowing the user to perform trades in which certain parameters normally thought of as “outputs” are varied over user-specified values.
Conventional approaches to such large optimization problems include performing a brute force search through the trade space, a task that is time consuming and impractical in many cases. While various multi-objective optimization algorithms have been employed in an attempt to overcome the combinatorial explosion problem associated with large trade spaces, it is extremely difficult to force the outputs of such algorithms to satisfy auxiliary conditions. It can be impractical to restrict the set of analyses to satisfy large sets of complex equality constraints.